Nonlinear Identification of Inverted Pendulum System Using Volterra Polynomials

Abstract

The inverted pendulum problem is one of the most important problems in control theory and has been studied excessively in control literatures. When control systems have strong requirements, the adjustment of the controller is a complex problem. The nonlinear model is useful for control design. In the present work, Volterra polynomial basis function (VPBF) networks have been used to identify a single inverted pendulum on a moving cart (SIPC) system. The inverted pendulum is a benchmark problem of nonlinear multivariable systems with inherent instability. The multivariable system has been considered with a force produced by a DC motor as the input, and four states variables as the outputs. A Fuzzy Logic controller has been used to stabilize the system for closed-loop identification. Here, the nonlinear model of the inverted pendulum has been implemented. The offline structure selection through orthogonal least square algorithm is used for the nonlinear system identification via the basis function selection of Volterra polynomial networks. The neural network is trained using the error between the model's outputs and the plant's actual outputs. The results show good match between predicted and actual outputs.